Patients who have not previously received imatinib mesylate receive oral imatinib mesylate on days 1-35. Patients who have previously received imatinib mesylate for at least 28 days receive oral imatinib mesylate on days 22-35. All patients receive daunorubicin IV over 2-3 minutes on days 1-3, vincristine IV over 1 minute on days 1, 8, 15, and 22, and oral prednisone on days 1-28. Patients with more than 5% residual blasts in bone marrow on day 28 receive a second course in the absence of disease progression or unacceptable toxicity.